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Displaying 421 – 440 of 501

Numerical solution of parabolic equations in high dimensions

Tobias Von Petersdorff, Christoph Schwab (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider the numerical solution of diffusion problems in $(0, T) \times Ω$ for $Ω \subset ℝ^{d}$ and for $T > 0$ in dimension $d \geq 1$ . We use a wavelet based sparse grid space discretization with mesh-width $h$ and order $p \geq 1$ , and $h p$ discontinuous Galerkin time-discretization of order $r = O (|log h|)$ on a geometric sequence of $O (|log h|)$ many time steps. The linear systems in each time step are solved iteratively by $O (|log h|)$ GMRES iterations with a wavelet preconditioner. We prove that this algorithm gives an $L^{2} (Ω)$ -error of $O (N^{- p})$ for $u (x, T)$ where $N$ is the total number of operations,...

Numerical solution of parabolic equations in high dimensions

Tobias von Petersdorff, Christoph Schwab (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the numerical solution of diffusion problems in (0,T) x Ω for $Ω \subset ℝ^{d}$ and for T > 0 in dimension dd ≥ 1. We use a wavelet based sparse grid space discretization with mesh-width h and order pd ≥ 1, and hp discontinuous Galerkin time-discretization of order $r = O (|log h|)$ on a geometric sequence of $O (|log h|)$ many time steps. The linear systems in each time step are solved iteratively by $O (|log h|)$ GMRES iterations with a wavelet preconditioner. We prove that this algorithm gives an L2(Ω)-error of O(N-p) for u(x,T)...

Numerical Solution of Retarded Initial Value Problems: Local and Global Error and Stepsize Control.

Herbert Arndt (1984)

Numerische Mathematik

Numerical solution of second order one-dimensional linear hyperbolic equation using trigonometric wavelets

Mahmood Jokar, Mehrdad Lakestani (2012)

Kybernetika

A numerical technique is presented for the solution of second order one dimensional linear hyperbolic equation. This method uses the trigonometric wavelets. The method consists of expanding the required approximate solution as the elements of trigonometric wavelets. Using the operational matrix of derivative, we reduce the problem to a set of algebraic linear equations. Some numerical example is included to demonstrate the validity and applicability of the technique. The method produces very accurate...

Numerical solution of second-order elliptic equations on plane domains

Lutz Angermann (1991)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Numerical solution of several models of internal transonic flow

Jaroslav Fořt, Karel Kozel (2003)

Applications of Mathematics

The paper deals with numerical solution of internal flow problems. It mentions a long tradition of mathematical modeling of internal flow, especially transonic flow at our department. Several models of flow based on potential equation, Euler equations, Navier-Stokes and Reynolds averaged Navier-Stokes equations with proper closure are considered. Some mathematical and numerical properties of the model are mentioned and numerical results achieved by in-house developed methods are presented.

Numerical solution of soap film dual problems.

Brakke, Kenneth A. (1995)

Experimental Mathematics

Numerical solution of some classes of complementarity and variational problems via dualization

Jochen W. Schmidt (1990)

Banach Center Publications

Numerical solution of some iterative differential equation

Jiří Kobza (1998)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Numerical Solution of Steady-State Porous Flow Free Boundary Problems.

H.W. Alt (1980/1981)

Numerische Mathematik

Numerical solution of Stokes problem for free convection effects in dissipative dusty medium.

Venkataraman, V., Kannan, K. (2004)

International Journal of Mathematics and Mathematical Sciences

Numerical solution of the Kiessl model

Josef Dalík, Josef Daněček, Jiří Vala (2000)

Applications of Mathematics

The Kiessl model of moisture and heat transfer in generally nonhomogeneous porous materials is analyzed. A weak formulation of the problem of propagation of the state parameters of this model, which are so-called moisture potential and temperature, is derived. An application of the method of discretization in time leads to a system of boundary-value problems for coupled pairs of nonlinear second order ODE’s. Some existence and regularity results for these problems are proved and an efficient numerical...

Numerical solution of the Maxwell equations in time-varying media using Magnus expansion

István Faragó, Ágnes Havasi, Robert Horváth (2012)

Open Mathematics

For the Maxwell equations in time-dependent media only finite difference schemes with time-dependent conductivity are known. In this paper we present a numerical scheme based on the Magnus expansion and operator splitting that can handle time-dependent permeability and permittivity too. We demonstrate our results with numerical tests.

Numerical Solution of the Obstacle Problem by the Penalty Method. Part II. Time-Dependent Problem.

Reinhard Scholz (1986)

Numerische Mathematik

Numerical Solution of the second Boundary value Problem in space

K. I. Iordanidis (1972)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Numerical solution of the second kind singular Volterra integral equations by modified Navot-Simpson's quadrature.

Araghi, Mohammad Ali Fariborzi, Kasmaei, Hamed Daei (2008)

International Journal of Open Problems in Computer Science and Mathematics. IJOPCM

Numerical Solution of Volterra Integral Equation.

J. Steinberg (1972)

Numerische Mathematik

Numerical Solution of Volterra Integral Equations.

E. Rakotch (1972/1973)

Numerische Mathematik

Numerical solutions for a model of tissue invasion and migration of tumour cells.

Kolev, M., Zubik-Kowal, B. (2011)

Computational & Mathematical Methods in Medicine

Numerical solutions for second-kind Volterra integral equations by Galerkin methods

Shu Hua Zhang, Yan Ping Lin, Ming Rao (2000)

Applications of Mathematics

In this paper, we study the global convergence for the numerical solutions of nonlinear Volterra integral equations of the second kind by means of Galerkin finite element methods. Global superconvergence properties are discussed by iterated finite element methods and interpolated finite element methods. Local superconvergence and iterative correction schemes are also considered by iterated finite element methods. We improve the corresponding results obtained by collocation methods in the recent...

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